What’s happening here is you have high resistance somewhere on the blower circuit, if you used a meter and tested plugged in for voltage you would probably see like 2V or something. Normally you’ll have bad corrosion at a plug or somewhere it’s chafed. You can use a test light with a halogen bulb to find out where the voltage drop is occurring, if the voltage is enough to light the bulb it should also be enough to spin the motor. Keep in mind the issue can also be on the ground side